Hainich with ERA-Interim

Manual fine tuning learning process for presentation 18 Jan 2023

%load_ext autoreload
%autoreload 2

from meteo_imp.kalman.fastai import *
from meteo_imp.kalman.filter import *
from meteo_imp.utils import *
from meteo_imp.data import *

from fastai.tabular.learner import *
from fastai.learner import *
from fastai.callback.all import *
from fastcore.foundation import L

from meteo_imp.kalman.fastai import show_results
import pandas as pd
import numpy as np
import torch

from sklearn.decomposition import PCA

reset_seed()

hai = pd.read_parquet(hai_path64)
hai_era = pd.read_parquet(hai_era_path64)

# dls = imp_dataloader(hai64, hai_era64, var_sel = gen_var_sel(['TA', 'SW_IN', 'VPD']), block_len=200, gap_len=10, bs=20, control_lags=[1])

pc = PCA().fit(hai)

d0 = hai.iloc[0:1]

tr0 = pc.transform(d0)

tr0

array([[-121.11917652,   -7.06844313,    0.87975241]])

t0 = np.random.randn(5,1) * 10
tt = np.hstack([t0, 2 * t0 + np.random.randn(5,1), 3 * t0 + np.random.randn(5,1)])

tt = np.vstack([tt, -tt])

tt.mean(0)

array([1.77635684e-16, 0.00000000e+00, 0.00000000e+00])

def pca(X):
    # Data matrix X, assumes 0-centered
    n, m = X.shape
    assert np.allclose(X.mean(axis=0), np.zeros(m))
    # Compute covariance matrix
    C = np.dot(X.T, X) / (n-1)
    # Eigen decomposition
    eigen_vals, eigen_vecs = np.linalg.eig(C)
    # Project X onto PC space
    X_pca = np.dot(X, eigen_vecs)
    return X_pca, eigen_vecs

pca(tt)

(array([[-9.15947487e+00, -3.03773243e-01,  3.81626348e-01],
        [ 2.00045215e+01, -1.99595583e-02,  1.53745860e+00],
        [ 1.33744310e+01,  2.01395206e-02, -3.19819214e-02],
        [-8.99057811e+00,  1.24208069e-01,  9.57988123e-01],
        [ 3.14616875e+01, -4.88141095e-02, -5.79117681e-01],
        [ 9.15947487e+00,  3.03773243e-01, -3.81626348e-01],
        [-2.00045215e+01,  1.99595583e-02, -1.53745860e+00],
        [-1.33744310e+01, -2.01395206e-02,  3.19819214e-02],
        [ 8.99057811e+00, -1.24208069e-01, -9.57988123e-01],
        [-3.14616875e+01,  4.88141095e-02,  5.79117681e-01]]),
 array([[-0.26545847, -0.95659856,  0.12021234],
        [-0.53518386,  0.04249433, -0.84366608],
        [-0.80194142,  0.28829401,  0.52323659]]))

sk_pc = PCA(2).fit(tt)

tt @ sk_pc.components_.T

array([[ -9.15947487,   0.38162635],
       [ 20.00452148,   1.5374586 ],
       [ 13.37443103,  -0.03198192],
       [ -8.99057811,   0.95798812],
       [ 31.46168754,  -0.57911768],
       [  9.15947487,  -0.38162635],
       [-20.00452148,  -1.5374586 ],
       [-13.37443103,   0.03198192],
       [  8.99057811,  -0.95798812],
       [-31.46168754,   0.57911768]])

tr = sk_pc.transform(tt)
tr

array([[ -9.15947487,   0.38162635],
       [ 20.00452148,   1.5374586 ],
       [ 13.37443103,  -0.03198192],
       [ -8.99057811,   0.95798812],
       [ 31.46168754,  -0.57911768],
       [  9.15947487,  -0.38162635],
       [-20.00452148,  -1.5374586 ],
       [-13.37443103,   0.03198192],
       [  8.99057811,  -0.95798812],
       [-31.46168754,   0.57911768]])

sk_pc.components_.T

array([[-0.26545847,  0.12021234],
       [-0.53518386, -0.84366608],
       [-0.80194142,  0.52323659]])

(sk_pc.components_ @ tt.T).T

array([[ -9.15947487,   0.38162635],
       [ 20.00452148,   1.5374586 ],
       [ 13.37443103,  -0.03198192],
       [ -8.99057811,   0.95798812],
       [ 31.46168754,  -0.57911768],
       [  9.15947487,  -0.38162635],
       [-20.00452148,  -1.5374586 ],
       [-13.37443103,   0.03198192],
       [  8.99057811,  -0.95798812],
       [-31.46168754,   0.57911768]])

tt[0, None]

array([[2.76792539, 4.56712931, 7.45746711]])

sk_pc.components_.shape

(3, 3)

tt[0].shape

(3,)

(sk_pc.components_ @ tt[0])

array([-9.15947487,  0.38162635])

tt[0]

array([2.76792539, 4.56712931, 7.45746711])

sk_pc.components_.T @ tr[0]

array([2.47733634, 4.58003795, 7.54504311])

sk_pc.inverse_transform(tr[0])

array([2.47733634, 4.58003795, 7.54504311])

d0.to_numpy()

array([[-0.6  ,  0.   ,  0.222]])

hai.iloc[0]

TA      -0.600
SW_IN    0.000
VPD      0.222
Name: 2000-01-01 00:30:00, dtype: float64

\[ x = y\Lambda \]

pc.components_

array([[ 0.01681572,  0.99979324,  0.01143269],
       [ 0.93010891, -0.01983747,  0.36674772],
       [-0.36689868, -0.00446652,  0.93025018]])

np.linalg.inv(pc.components_)

array([[ 0.01681572,  0.93010891, -0.36689868],
       [ 0.99979324, -0.01983747, -0.00446652],
       [ 0.01143269,  0.36674772,  0.93025018]])

assuming that the control has the same dimensions of the observations then if we are doing a local slope model we have \(B \in \mathbb{R}^{state \times contr}\): \[ B = \begin{bmatrix} -I & I \\ 0 & 0 \end{bmatrix}\]

from torch import hstack, eye, vstack, ones, zeros, tensor
from functools import partial

def set_dtype(*args, dtype=torch.float64):
    return [partial(arg, dtype=dtype) for arg in args] 

eye, ones, zeros, tensor = set_dtype(eye, ones, zeros, tensor)

def init_smart(n_dim_obs, n_dim_state, df, pca=True):
    # n_dim_obs == n_dim_contr
    if pca:
        comp = PCA(n_dim_state).fit(df).components_
        obs_matrix = tensor(comp.T) # transform state -> obs
        contr_matrix = tensor(comp) # transform obs -> state
    else:
        obs_matrix, contr_matrix = eye(n_dim_obs), eye(n_dim_obs)
        
    return KalmanFilter(
        trans_matrix =     vstack([hstack([eye(n_dim_state),                eye(n_dim_state)]),
                                   hstack([zeros(n_dim_state, n_dim_state), eye(n_dim_state)])]),
        trans_off =        zeros(n_dim_state * 2),        
        trans_cov =        eye(n_dim_state * 2)*.1,        
        obs_matrix =       hstack([obs_matrix, zeros(n_dim_obs, n_dim_state)]),
        obs_off =          zeros(n_dim_obs),          
        obs_cov =          eye(n_dim_obs)*.01,            
        contr_matrix =     vstack([hstack([-contr_matrix,                  contr_matrix]),
                                   hstack([ zeros(n_dim_state,n_dim_obs), zeros(n_dim_state, n_dim_obs)])]),
        init_state_mean =  zeros(n_dim_state * 2),        
        init_state_cov =   eye(n_dim_state * 2) * 3,
    ) 

np.hstack([np.eye(2), np.eye(2)])

array([[1., 0., 1., 0.],
       [0., 1., 0., 1.]])

init_smart(3,2, hai)

Kalman Filter (3 obs, 4 state, 6 contr)

trans matrix (A)

state	x_0	x_1	x_2	x_3
x_0	1.0000	0.0000	1.0000	0.0000
x_1	0.0000	1.0000	0.0000	1.0000
x_2	0.0000	0.0000	1.0000	0.0000
x_3	0.0000	0.0000	0.0000	1.0000

trans cov (Q)

state	x_0	x_1	x_2	x_3
x_0	0.1000	0.0000	0.0000	0.0000
x_1	0.0000	0.1000	0.0000	0.0000
x_2	0.0000	0.0000	0.1000	0.0000
x_3	0.0000	0.0000	0.0000	0.1000

trans off

state	offset
x_0	0.0000
x_1	0.0000
x_2	0.0000
x_3	0.0000

obs matrix (H)

variable	x_0	x_1	x_2	x_3
y_0	0.0168	0.9301	0.0000	0.0000
y_1	0.9998	-0.0198	0.0000	0.0000
y_2	0.0114	0.3667	0.0000	0.0000

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0100	0.0000	0.0000
y_1	0.0000	0.0100	0.0000
y_2	0.0000	0.0000	0.0100

obs off

variable	offset
y_0	0.0000
y_1	0.0000
y_2	0.0000

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.0168	-0.9998	-0.0114	0.0168	0.9998	0.0114
x_1	-0.9301	0.0198	-0.3667	0.9301	-0.0198	0.3667
x_2	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
x_3	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

init state mean

state	mean
x_0	0.0000
x_1	0.0000
x_2	0.0000
x_3	0.0000

init state cov

state	x_0	x_1	x_2	x_3
x_0	3.0000	0.0000	0.0000	0.0000
x_1	0.0000	3.0000	0.0000	0.0000
x_2	0.0000	0.0000	3.0000	0.0000
x_3	0.0000	0.0000	0.0000	3.0000

class PersistentRecorder(Callback):
    order = 70
    name = "per_recorder"
    attrs = ['lrs', 'iters', 'losses', 'values']
    def before_fit(self):
        "Prepare state for training"
        for attr in self.attrs:
            if not hasattr(self.per_recorder, attr): setattr(self.per_recorder, attr, [])

    def after_batch(self):
        for attr in self.attrs:
            setattr(self.per_recorder, attr, getattr(self.recorder, attr))

models = []

dls = imp_dataloader(hai, hai_era, var_sel = ['TA', 'SW_IN', 'VPD'], block_len=200, gap_len=10, bs=20, control_lags=[1], n_rep=2)

len(dls.valid.items)
items = [dls.valid.items[i] for i in [10, 50, 100, 200, 300, 400]]

def train_show_save(learn, n_iter, lr):
    learn.fit(n_iter, lr)
    models.append(learn.model.state_dict().copy())
    learn.recorder.plot_loss()
    items = [dls.valid.items[i] for i in [10, 50, 100, 200, 300, 400]]
    return show_results(learn, items = items, control=hai_control)

Gaps all variables

model = init_smart(3,3,3, hai, pca=False).cuda()

loss = loss_func=KalmanLoss(only_gap=False)
learn = Learner(dls, model, loss, cbs=[Float64Callback], metrics=imp_metrics)

learn.model.use_smooth = True

show_results(learn, items=items, control=hai_control)

train_show_save(learn, 1, 1e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	-87.370314	-96.212915	0.069196	0.210351	0.946861	-250571814513532732431918956544.000000	02:37

trans matrix (A)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	1.1489	0.0042	0.0120	0.8404	-0.0794	-0.1127
x_1	-0.0954	1.1464	-0.0546	0.1177	0.8560	0.0599
x_2	-0.0225	0.0420	1.1357	-0.0717	-0.1190	0.8475
x_3	0.1201	0.0661	0.1170	1.1840	-0.1150	-0.1073
x_4	0.0770	0.1299	0.0068	-0.1847	1.0987	-0.1500
x_5	0.1084	0.0358	0.1133	-0.1809	-0.0281	1.1533

trans cov (Q)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	0.0341	0.0493	0.0361	-0.0008	-0.0312	0.0026
x_1	0.0493	0.1125	0.0531	0.0475	0.0047	0.0509
x_2	0.0361	0.0531	0.0399	0.0001	-0.0327	0.0058
x_3	-0.0008	0.0475	0.0001	0.0608	0.0614	0.0585
x_4	-0.0312	0.0047	-0.0327	0.0614	0.0901	0.0554
x_5	0.0026	0.0509	0.0058	0.0585	0.0554	0.0594

trans off

state	offset
x_0	0.0008
x_1	-0.0083
x_2	0.0067
x_3	0.0023
x_4	-0.0007
x_5	0.0005

obs matrix (H)

variable	x_0	x_1	x_2	x_3	x_4	x_5
y_0	0.8238	-0.1897	-0.1014	-0.0841	0.1914	0.1286
y_1	0.0814	0.8353	0.1048	0.1040	0.0127	0.0689
y_2	-0.0742	-0.1502	0.8296	0.1282	0.1811	-0.0746

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0084	0.0000	0.0000
y_1	0.0000	0.0084	0.0000
y_2	0.0000	0.0000	0.0084

obs off

variable	offset
y_0	0.0017
y_1	-0.0046
y_2	0.0026

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-1.0290	-0.0485	-0.0022	0.9297	0.0792	-0.0247
x_1	-0.0267	-0.8778	-0.0233	0.0113	0.9099	0.0261
x_2	-0.0018	-0.0592	-1.0044	-0.0310	0.0674	0.9204
x_3	-0.0503	-0.0312	-0.0556	-0.0440	-0.0529	-0.0587
x_4	-0.0375	-0.0537	-0.0246	-0.0412	-0.0352	-0.0338
x_5	-0.0653	-0.0179	-0.0575	-0.0655	-0.0307	-0.0449

init state mean

state	mean
x_0	-0.0393
x_1	0.0044
x_2	-0.0092
x_3	0.0207
x_4	-0.0094
x_5	-0.0021

init state cov

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	2.5500	-0.1402	-0.0082	0.5233	0.3011	0.0882
x_1	-0.1402	2.4578	0.1502	0.0355	0.5714	-0.0459
x_2	-0.0082	0.1502	2.5045	0.2739	0.0634	0.5195
x_3	0.5233	0.0355	0.2739	2.3814	-0.2201	-0.1842
x_4	0.3011	0.5714	0.0634	-0.2201	2.3880	-0.1162
x_5	0.0882	-0.0459	0.5195	-0.1842	-0.1162	2.3874

train_show_save(learn, 1, 1e-3)

/home/simone/anaconda3/envs/data-science/lib/python3.10/site-packages/fastai/callback/core.py:69: UserWarning: You are shadowing an attribute (__class__) that exists in the learner. Use `self.learn.__class__` to avoid this
  warn(f"You are shadowing an attribute ({name}) that exists in the learner. Use `self.learn.{name}` to avoid this")

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	-108.023250	-113.113034	0.073622	0.198386	0.956828	-105578612000578019271909572608.000000	02:37

trans matrix (A)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	1.1440	-0.0057	0.0107	0.8262	-0.0845	-0.1205
x_1	-0.0534	1.2089	-0.0223	0.0948	0.7937	0.0494
x_2	-0.0289	0.0176	1.1417	-0.0702	-0.1154	0.8351
x_3	0.1277	0.0589	0.1074	1.1787	-0.1203	-0.1024
x_4	0.0654	0.1560	0.0043	-0.1781	1.1087	-0.1415
x_5	0.0959	0.0439	0.1197	-0.1725	-0.0340	1.1496

trans cov (Q)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	0.0207	0.0254	0.0210	-0.0052	-0.0232	-0.0033
x_1	0.0254	0.0548	0.0255	0.0259	0.0034	0.0281
x_2	0.0210	0.0255	0.0222	-0.0056	-0.0241	-0.0023
x_3	-0.0052	0.0259	-0.0056	0.0473	0.0504	0.0465
x_4	-0.0232	0.0034	-0.0241	0.0504	0.0695	0.0473
x_5	-0.0033	0.0281	-0.0023	0.0465	0.0473	0.0477

trans off

state	offset
x_0	0.0004
x_1	-0.0055
x_2	0.0048
x_3	0.0027
x_4	-0.0033
x_5	0.0021

obs matrix (H)

variable	x_0	x_1	x_2	x_3	x_4	x_5
y_0	0.7902	-0.2032	-0.1217	-0.0986	0.2164	0.1090
y_1	0.0160	0.7417	0.0555	0.1016	0.1041	0.0374
y_2	-0.1103	-0.1594	0.7916	0.1185	0.2096	-0.0949

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0077	0.0000	0.0000
y_1	0.0000	0.0077	0.0000
y_2	0.0000	0.0000	0.0077

obs off

variable	offset
y_0	-0.0009
y_1	-0.0053
y_2	-0.0021

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-1.0277	-0.0595	-0.0019	0.9181	0.0838	-0.0194
x_1	-0.0414	-0.8661	-0.0323	0.0110	0.8741	0.0262
x_2	-0.0029	-0.0647	-1.0045	-0.0319	0.0757	0.8957
x_3	-0.0678	-0.0368	-0.0564	-0.0559	-0.0610	-0.0639
x_4	-0.0374	-0.0690	-0.0209	-0.0485	-0.0406	-0.0354
x_5	-0.0591	-0.0267	-0.0753	-0.0633	-0.0407	-0.0555

init state mean

state	mean
x_0	-0.0396
x_1	-0.0009
x_2	-0.0049
x_3	0.0153
x_4	-0.0139
x_5	-0.0094

init state cov

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	2.6364	-0.1456	-0.0020	0.5695	0.3986	0.1628
x_1	-0.1456	2.3292	0.1064	0.2074	0.7591	0.1475
x_2	-0.0020	0.1064	2.4205	0.3489	0.1488	0.6143
x_3	0.5695	0.2074	0.3489	2.2351	-0.4355	-0.3277
x_4	0.3986	0.7591	0.1488	-0.4355	2.1625	-0.3445
x_5	0.1628	0.1475	0.6143	-0.3277	-0.3445	2.2518

# learn.save("17_jan_all_gaps")

Path('models/17_jan_all_gaps.pth')

train_show_save(learn, 2, 1e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	-122.620241	-126.621236	0.077944	0.202366	0.948695	-115274990280631988956159803392.000000	02:38
1	-134.455010	-139.768441	0.074152	0.188695	0.959962	-103653315974387814635399020544.000000	02:31

trans matrix (A)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	1.1347	-0.0147	0.0100	0.8021	-0.1122	-0.1444
x_1	-0.0388	1.2480	-0.0185	0.0773	0.7576	0.0414
x_2	-0.0257	-0.0018	1.1500	-0.0814	-0.1272	0.8203
x_3	0.1332	0.0451	0.0866	1.1612	-0.1103	-0.0917
x_4	0.0559	0.1720	0.0056	-0.1625	1.1052	-0.1248
x_5	0.0721	0.0457	0.1226	-0.1523	-0.0385	1.1357

trans cov (Q)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	0.0146	0.0183	0.0142	-0.0081	-0.0202	-0.0067
x_1	0.0183	0.0445	0.0187	0.0148	-0.0014	0.0168
x_2	0.0142	0.0187	0.0143	-0.0065	-0.0187	-0.0044
x_3	-0.0081	0.0148	-0.0065	0.0340	0.0393	0.0343
x_4	-0.0202	-0.0014	-0.0187	0.0393	0.0550	0.0378
x_5	-0.0067	0.0168	-0.0044	0.0343	0.0378	0.0361

trans off

state	offset
x_0	0.0014
x_1	-0.0059
x_2	0.0039
x_3	0.0016
x_4	-0.0036
x_5	0.0032

obs matrix (H)

variable	x_0	x_1	x_2	x_3	x_4	x_5
y_0	0.7310	-0.1642	-0.0983	-0.1030	0.2236	0.0907
y_1	0.0158	0.6777	0.0705	0.1196	0.1642	0.0316
y_2	-0.1124	-0.1249	0.7399	0.1211	0.2193	-0.0846

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0064	0.0000	0.0000
y_1	0.0000	0.0065	0.0000
y_2	0.0000	0.0000	0.0065

obs off

variable	offset
y_0	-0.0019
y_1	-0.0046
y_2	-0.0026

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-1.0316	-0.0708	-0.0019	0.8851	0.0973	-0.0094
x_1	-0.0727	-0.8659	-0.0584	0.0075	0.7964	0.0142
x_2	0.0098	-0.0734	-1.0045	-0.0156	0.0845	0.8489
x_3	-0.0977	-0.0434	-0.0574	-0.0723	-0.0760	-0.0730
x_4	-0.0309	-0.1114	-0.0185	-0.0559	-0.0634	-0.0420
x_5	-0.0503	-0.0424	-0.1056	-0.0644	-0.0571	-0.0729

init state mean

state	mean
x_0	-0.0585
x_1	-0.0141
x_2	-0.0070
x_3	0.0239
x_4	-0.0043
x_5	-0.0069

init state cov

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	2.9257	0.1245	0.1987	0.4475	0.2435	0.0893
x_1	0.1245	2.4393	0.3641	0.2107	0.7802	0.1895
x_2	0.1987	0.3641	2.4862	0.2959	0.0089	0.6053
x_3	0.4475	0.2107	0.2959	2.1058	-0.5771	-0.4644
x_4	0.2435	0.7802	0.0089	-0.5771	1.9818	-0.5064
x_5	0.0893	0.1895	0.6053	-0.4644	-0.5064	2.0952

train_show_save(learn, 2, 1e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	-149.288297	-152.804403	0.072760	0.179190	0.956827	-61340364986143763995601928192.000000	02:35
1	-160.099637	-165.002097	0.071263	0.181697	0.963587	-48387608947773502947627892736.000000	02:37

# learn.save("17_jan_all_gaps_final")

Path('models/17_jan_all_gaps_final.pth')

p = show_results(learn, control=hai_control, items = [items[i] for i in [0,5,4]])

Gap in only 1 variable

dls2 = imp_dataloader(hai, hai_era, var_sel = ['TA'], block_len=200, gap_len=10, bs=20, control_lags=[1], n_rep=2)

model2 = init_smart(3,3, hai, pca=True).cuda()

loss2 = loss_func=KalmanLoss(only_gap=False)
learn2 = Learner(dls2, model2, loss, cbs=[Float64Callback], metrics=imp_metrics)

train_show_save(learn2, 1, 1e-3)

0.00% [0/1 00:00<?]

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time

0.00% [0/91 00:00<?]

NotImplementedError: Module [KalmanFilter] is missing the required "forward" function

Disable smoother

model.use_smooth = False

train_show_save(learn, 3, 1e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	534.159578	465.194522	0.284379	0.329570	-1.919198	-241825956681560181426503024640.000000	02:24

trans matrix (A)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	0.6761	0.1157	-0.0095	0.5895	0.0728	0.0850
x_1	0.0309	0.6675	0.1639	0.2296	0.5542	-0.1129
x_2	0.1836	-0.1476	0.6498	0.1684	-0.2142	0.5899
x_3	-0.1246	0.0361	0.0138	0.6844	-0.0830	0.1501
x_4	-0.0167	-0.0399	0.0044	0.0089	0.7537	0.0580
x_5	0.0341	0.0300	-0.0436	-0.0362	0.2878	0.6487

trans cov (Q)

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	0.5106	0.3768	0.4383	-0.1720	-0.2863	-0.1749
x_1	0.3768	0.5687	0.1931	-0.2781	0.0461	0.0798
x_2	0.4383	0.1931	0.4406	-0.0734	-0.3650	-0.2384
x_3	-0.1720	-0.2781	-0.0734	0.5150	0.3608	0.3418
x_4	-0.2863	0.0461	-0.3650	0.3608	0.8281	0.6975
x_5	-0.1749	0.0798	-0.2384	0.3418	0.6975	0.6156

trans off

state	offset
x_0	-0.0166
x_1	-0.0196
x_2	-0.0446
x_3	0.0033
x_4	-0.0022
x_5	0.0107

obs matrix (H)

variable	x_0	x_1	x_2	x_3	x_4	x_5
y_0	-0.3096	0.5414	-0.0652	0.4906	-0.0643	-0.3834
y_1	0.6288	-0.3366	-0.3681	0.0321	-0.2062	0.3634
y_2	-0.2813	0.0500	0.4738	-0.0601	0.2872	-0.1334

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.3678	0.0000	0.0000
y_1	0.0000	0.3707	0.0000
y_2	0.0000	0.0000	0.3693

obs off

variable	offset
y_0	-0.0197
y_1	-0.0452
y_2	-0.0451

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.9410	-0.5681	-0.8722	0.9998	1.2958	1.0828
x_1	-0.7019	-0.7354	-0.9277	1.2348	1.1344	0.9620
x_2	-0.9322	-0.7328	-0.8307	1.0310	1.1112	1.1017
x_3	0.0914	0.2592	0.0286	0.0638	0.1644	-0.0007
x_4	0.2175	-0.0398	0.0226	0.2072	-0.1205	-0.0117
x_5	-0.0578	0.1485	0.0908	-0.0613	0.0627	0.0792

init state mean

state	mean
x_0	0.0290
x_1	-0.0320
x_2	-0.0494
x_3	0.0296
x_4	0.0387
x_5	0.1010

init state cov

state	x_0	x_1	x_2	x_3	x_4	x_5
x_0	3.7171	2.7054	2.8366	2.0078	1.3904	2.3275
x_1	2.7054	4.5189	2.1010	1.4436	1.8804	2.8057
x_2	2.8366	2.1010	3.3027	1.3323	0.9307	2.0280
x_3	2.0078	1.4436	1.3323	3.3867	2.1461	3.0821
x_4	1.3904	1.8804	0.9307	2.1461	2.5441	2.6815
x_5	2.3275	2.8057	2.0280	3.0821	2.6815	3.7653

IndexError: list index out of range

train_show_save(learn, 1, 1e-2)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	272.526685	207.314376	0.279615	0.290300	-3.962859	-113462721102480788295669252096.000000	06:35

trans matrix (A)

state	x_0	x_1	x_2
x_0	0.5320	0.0984	0.2567
x_1	0.5386	-0.1615	-0.1019
x_2	0.4759	0.4640	0.4202

trans cov (Q)

state	x_0	x_1	x_2
x_0	1.4043	0.5126	1.8864
x_1	0.5126	0.1871	0.6885
x_2	1.8864	0.6885	2.5339

trans off

state	offset
x_0	-0.0972
x_1	-0.2735
x_2	0.0298

obs matrix (H)

variable	x_0	x_1	x_2
y_0	0.1792	0.7014	-0.3164
y_1	-0.5045	0.1311	0.3455
y_2	-0.0962	0.0705	0.1246

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0190	0.0000	0.0000
y_1	0.0000	0.1624	0.0000
y_2	0.0000	0.0000	0.0297

obs off

variable	offset
y_0	0.1664
y_1	-0.0433
y_2	0.0232

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.0331	-0.4960	0.2924	0.5946	-0.1127	-0.1933
x_1	0.5991	0.3053	0.2248	0.7649	0.9446	0.0394
x_2	0.0060	0.0013	-0.0667	-0.1143	0.7781	0.6409

init state mean

state	mean
x_0	-1.0627
x_1	-0.6392
x_2	-1.2803

init state cov

state	x_0	x_1	x_2
x_0	9.0224	3.6789	10.5469
x_1	3.6789	2.3654	5.9687
x_2	10.5469	5.9687	21.9915

NameError: name 'learn1' is not defined

train_show_save(learn, 1, 2e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	160.675568	150.361449	0.266633	0.269324	-1.959343	-53151966368643636872563654656.000000	05:30

trans matrix (A)

state	x_0	x_1	x_2
x_0	0.5363	0.1070	0.2723
x_1	0.5375	-0.1534	-0.0948
x_2	0.4909	0.4638	0.4301

trans cov (Q)

state	x_0	x_1	x_2
x_0	1.3408	0.4970	1.7922
x_1	0.4970	0.1842	0.6643
x_2	1.7922	0.6643	2.3955

trans off

state	offset
x_0	-0.0948
x_1	-0.2568
x_2	0.0393

obs matrix (H)

variable	x_0	x_1	x_2
y_0	0.1742	0.6954	-0.3174
y_1	-0.5094	0.1551	0.3429
y_2	-0.1147	0.0583	0.1163

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0121	0.0000	0.0000
y_1	0.0000	0.1100	0.0000
y_2	0.0000	0.0000	0.0190

obs off

variable	offset
y_0	0.1697
y_1	-0.0123
y_2	0.0387

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.0363	-0.5225	0.3103	0.5948	-0.0692	-0.1628
x_1	0.5955	0.3523	0.1332	0.7587	0.9820	-0.0509
x_2	-0.0159	0.0573	-0.0471	-0.1409	0.7802	0.6457

init state mean

state	mean
x_0	-1.0500
x_1	-0.6014
x_2	-1.2993

init state cov

state	x_0	x_1	x_2
x_0	10.9221	3.8061	12.4742
x_1	3.8061	1.7574	5.6427
x_2	12.4742	5.6427	24.9669

train_show_save(learn, 1, 2e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	115.738528	104.632719	0.257947	0.259673	-1.679687	-24519279833493970234084687872.000000	05:09

trans matrix (A)

state	x_0	x_1	x_2
x_0	0.5303	0.1124	0.2795
x_1	0.5333	-0.1470	-0.0908
x_2	0.4963	0.4602	0.4322

trans cov (Q)

state	x_0	x_1	x_2
x_0	1.2399	0.4645	1.6526
x_1	0.4645	0.1740	0.6191
x_2	1.6526	0.6191	2.2026

trans off

state	offset
x_0	-0.0883
x_1	-0.2505
x_2	0.0440

obs matrix (H)

variable	x_0	x_1	x_2
y_0	0.1715	0.6898	-0.3162
y_1	-0.5142	0.1782	0.3403
y_2	-0.1173	0.0543	0.1176

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0079	0.0000	0.0000
y_1	0.0000	0.0732	0.0000
y_2	0.0000	0.0000	0.0124

obs off

variable	offset
y_0	0.1699
y_1	-0.0058
y_2	0.0383

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.0449	-0.5621	0.3391	0.5937	0.0285	-0.1154
x_1	0.5860	0.3917	0.0584	0.7468	1.0129	-0.1247
x_2	-0.0479	0.1664	-0.0280	-0.1814	0.7807	0.6422

init state mean

state	mean
x_0	-1.0488
x_1	-0.5958
x_2	-1.3038

init state cov

state	x_0	x_1	x_2
x_0	12.1503	4.1501	13.5248
x_1	4.1501	1.7544	5.9730
x_2	13.5248	5.9730	27.6423

learn.model.use_smooth = True
show_results(learn, items = [learn.dls.valid.items[i] for i in [10, 100, 300, 500, 700, 1000]])

train_show_save(learn, 1, 1e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	30.829145	26.059960	0.201186	0.215770	-0.034140	-48287381455002891037683220480.000000	06:32

trans matrix (A)

state	x_0	x_1	x_2
x_0	0.5309	0.1159	0.2797
x_1	0.5313	-0.1385	-0.0881
x_2	0.4961	0.4560	0.4324

trans cov (Q)

state	x_0	x_1	x_2
x_0	1.1473	0.4769	1.5832
x_1	0.4769	0.2008	0.6682
x_2	1.5832	0.6682	2.2249

trans off

state	offset
x_0	-0.0894
x_1	-0.2426
x_2	0.0426

obs matrix (H)

variable	x_0	x_1	x_2
y_0	0.1711	0.6883	-0.3146
y_1	-0.5151	0.1887	0.3414
y_2	-0.1155	0.0454	0.1145

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0063	0.0000	0.0000
y_1	0.0000	0.0583	0.0000
y_2	0.0000	0.0000	0.0097

obs off

variable	offset
y_0	0.1747
y_1	0.0044
y_2	0.0287

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.0475	-0.5920	0.3650	0.5948	0.0563	-0.0801
x_1	0.5812	0.4322	-0.0088	0.7377	1.0076	-0.1962
x_2	-0.0461	0.1875	-0.0228	-0.1820	0.7675	0.6408

init state mean

state	mean
x_0	-1.0477
x_1	-0.5959
x_2	-1.2990

init state cov

state	x_0	x_1	x_2
x_0	12.4282	4.5316	13.6935
x_1	4.5316	2.1406	6.4461
x_2	13.6935	6.4461	27.6478

train_show_save(learn, 1, 1e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	2.643850	-2.886783	0.193556	0.212050	0.165402	-29540765662186335322106757120.000000	06:27

trans matrix (A)

state	x_0	x_1	x_2
x_0	0.5339	0.1210	0.2783
x_1	0.5270	-0.1285	-0.0862
x_2	0.4976	0.4502	0.4350

trans cov (Q)

state	x_0	x_1	x_2
x_0	1.0913	0.4682	1.5174
x_1	0.4682	0.2037	0.6628
x_2	1.5174	0.6628	2.1595

trans off

state	offset
x_0	-0.0873
x_1	-0.2397
x_2	0.0401

obs matrix (H)

variable	x_0	x_1	x_2
y_0	0.1690	0.6841	-0.3145
y_1	-0.5175	0.1944	0.3405
y_2	-0.1099	0.0372	0.1142

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0051	0.0000	0.0000
y_1	0.0000	0.0467	0.0000
y_2	0.0000	0.0000	0.0078

obs off

variable	offset
y_0	0.1766
y_1	0.0070
y_2	0.0210

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.0614	-0.6233	0.4026	0.5869	0.0964	-0.0301
x_1	0.5842	0.4624	-0.0654	0.7358	0.9837	-0.2582
x_2	-0.0390	0.2132	-0.0130	-0.1775	0.7580	0.6438

init state mean

state	mean
x_0	-1.0447
x_1	-0.5957
x_2	-1.2961

init state cov

state	x_0	x_1	x_2
x_0	13.1380	4.8428	14.4531
x_1	4.8428	2.3677	6.8288
x_2	14.4531	6.8288	28.0978

Loss only gap

learn.model.use_smooth = True
learn.loss_func = KalmanLoss(only_gap=True)

train_show_save(learn, 1,  5e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	-3.892116	-2.872949	0.120294	0.204105	-2.923830	-85436991145187843135533744128.000000	04:26

trans matrix (A)

state	x_0	x_1	x_2
x_0	0.2027	0.3761	0.2969
x_1	0.3594	0.3686	0.3606
x_2	0.4679	0.2295	0.2852

trans cov (Q)

state	x_0	x_1	x_2
x_0	0.0220	0.0113	-0.0224
x_1	0.0113	0.0064	-0.0097
x_2	-0.0224	-0.0097	0.0290

trans off

state	offset
x_0	0.3025
x_1	-0.5231
x_2	0.2064

obs matrix (H)

variable	x_0	x_1	x_2
y_0	-0.1489	0.3517	-0.0053
y_1	0.2922	0.1890	-0.4105
y_2	0.3920	-0.0638	0.2473

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0001	0.0000	0.0000
y_1	0.0000	0.0054	0.0000
y_2	0.0000	0.0000	0.0003

obs off

variable	offset
y_0	0.2038
y_1	0.1323
y_2	-0.1988

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-0.9856	0.6178	0.4694	-0.5368	0.5367	-0.0159
x_1	0.6667	0.5327	-0.3882	0.6907	-0.0209	-0.2365
x_2	0.0330	-0.7175	-0.1714	0.2048	-0.6491	0.1349

init state mean

state	mean
x_0	0.0922
x_1	-0.6262
x_2	0.2368

init state cov

state	x_0	x_1	x_2
x_0	8.1062	12.7070	6.0908
x_1	12.7070	21.6312	10.2860
x_2	6.0908	10.2860	5.5679

Smoother

learn1.model.use_smooth = True

train_show_save(learn1, 1,  5e-3)

epoch	train_loss	valid_loss	rmse	rmse_gap	r2	r2_gap	time
0	-415.543654	-449.643886	0.055635	0.200575	0.759219	-45104963579554009935054372864.000000	07:43

trans matrix (A)

state	x_0	x_1	x_2
x_0	0.1815	0.3765	0.3138
x_1	0.3401	0.3500	0.3764
x_2	0.4904	0.2297	0.2438

trans cov (Q)

state	x_0	x_1	x_2
x_0	0.0491	0.0170	-0.0614
x_1	0.0170	0.0127	-0.0243
x_2	-0.0614	-0.0243	0.0889

trans off

state	offset
x_0	0.3080
x_1	-0.5210
x_2	0.2044

obs matrix (H)

variable	x_0	x_1	x_2
y_0	-0.1630	0.3552	-0.0202
y_1	0.3143	0.1963	-0.4623
y_2	0.4022	-0.0653	0.2466

obs cov (R)

variable	y_0	y_1	y_2
y_0	0.0001	0.0000	0.0000
y_1	0.0000	0.0054	0.0000
y_2	0.0000	0.0000	0.0003

obs off

variable	offset
y_0	0.2096
y_1	0.1459
y_2	-0.2079

contr matrix (B)

state	c_0	c_1	c_2	c_3	c_4	c_5
x_0	-1.0006	0.5988	0.4673	-0.5447	0.5317	-0.0122
x_1	0.6825	0.5156	-0.3620	0.7188	-0.0186	-0.1805
x_2	0.0303	-0.7130	-0.1672	0.2100	-0.6278	0.1642

init state mean

state	mean
x_0	0.0933
x_1	-0.6332
x_2	0.2392

init state cov

state	x_0	x_1	x_2
x_0	8.2929	13.0004	6.2311
x_1	13.0004	22.1310	10.5205
x_2	6.2311	10.5205	5.6921

# learn1.save("model_16_jan1")

Path('models/model_16_jan1.pth')